Question

Someone PLEASE HELP!!!
I've been stuck for HOURS. I will work with you, I don't just want the answer, I need to know how and why. PLEASE!!!

What is a40 for the arithmetic sequence presented in the table below?

n 8 12
an 60 48

Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference.

Answer 1

you can think of an arithmetic sequence as a line. So then (n, an) would be a point on the line. So start by finding the equation of the line that goes through (8, 60) and (12, 48). Do you know how to do that?

Answer 2

The slope is the d value right? So would it be -3?

Answer 3

yes

Answer 4

Okay so what now? Is a1 8?

Answer 5

They didn't actually give you a1.
You can actually start this in point slope form, then back out an equation for the sequence

y -y1 = m(x-x1)

or with your terms

an - a8 = d(n - 8)

the 12 can replace the 8 just as easily

Answer 6

does that make sense?

Answer 7

It makes sense but I've only been given one formula, the one listed above. This is the first lesson of the chapter, so I'd like to solve it the way they want me to. I really appreciate your help, btw. I'm just so stuck. I've done other problems using this formula successfully and I don't know why this question is so confusing.

Answer 8

this one can't be solved with that formula alone because that formula requires you to have the 1st term of the sequence. You were given the 8th and 12th terms. So you have to either write the sequence using the 8th and 12th terms (above) or back out the 1st term by subtracting -3 from the 8th and subsequent terms

Answer 9

What would be the value of n? My answer choices for a40 are -44, -40, -36, and -26.

Answer 10

ok maybe let's try it this way. We know the 8th term is 60 and d is -3, so you can solve for the 1st term

\[a_8=a_1+d(n-1)\]
\[60=a_1-3(8-1)\]
Solve that for \(a_1\)

Answer 11

So the first term is 81 then. I worked backwards and figured that out previously, but I still don't know what to do for n.

Answer 12

n is 40

Answer 13

because they ask for a40

Answer 14

so then you can you your formula
\[a_n=a_1+d(n-1)\]
\[a_{40}=81-3(40-1)\]

Answer 15

so a40=81-3(40-1)
a40=81-117
a40=-36

Answer 16

yes

Answer 17

For like three hours I've been adding in an extra - sign and getting 198. Thank you so much for your help!!! How do I give you a medal?

Answer 18

you're welcome. seems like you figured it out :)

Answer 19

If I have any questions in the future, would you mind if I tag you?